Coarse equivalence versus bijective coarse equivalence of expander graphs

Coarse equivalence versus bijective coarse equivalence of expander graphs

We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras of coarse disjoint unions of expanders graphs are isomorphic, then the metric spaces must be b...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Mathematische Zeitschrift 2024-07, Vol.307 (3), Article 44
Hauptverfasser: Baudier, Florent P., Braga, Bruno M., Farah, Ilijas, Vignati, Alessandro, Willett, Rufus
Format: Artikel
Sprache:eng
Schlagworte:
Equivalence
Expanders
Graphs
Mathematics
Mathematics and Statistics
Metric space
Unions
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:We provide a characterization of when a coarse equivalence between coarse disjoint unions of expander graphs is close to a bijective coarse equivalence. We use this to show that if the uniform Roe algebras of coarse disjoint unions of expanders graphs are isomorphic, then the metric spaces must be bijectively coarsely equivalent.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-024-03512-w